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Name ______________________ MATH 1090 FINAL EXAM instructor:. date Dec. 2006 2 hours with calculator section / time:.
Work problems completely, either on this paper, or on another sheet, which you include with this paper. Credit will be given for work. Circling correct answer without work to support the answer will not receive credit. If you turn in work on another paper, number the problems so they can be found and read. If you answer โnone of the preceding,โ tell what the answer should be.
Work 15 of the18 problems on this exam. Mark out the 3 problems that will not be graded. The first 15 not marked out will be scored.
- A company charting its profits notices that the relationship between the number of units sold, x , and
the profit P is linear. If 120 units sold results in $7400 profit and 180 units results in $12, profit, identify the equation that models its profit.
a) P ( x ) = 17,850 โ 61.67 x b) P ( x ) = 0.012 x โ 12,347.82 c) P ( x ) = 1652 x + 738116
d) P ( x ) = 82.5 x โ 2500 e) P ( x ) = 17,300 โ 82.5 x f ) none of the preceding
- The monthly profit from producing and selling x units of a product is given by the equation
P ( x ) = โ 0.2 x^2 + 24 x โ 180. Producing and selling how many units will result in a profit for this product?
a) 7 < x < 127 b) 9 < x < 111 c) x > 112
d) x = 60 e) x = 540 f ) none of the preceding
- Annual sales S (in $100,000) are related to advertising expenses x (in $10,000) according to the
function x
x S x 24 0. 8
=. Determine the maximum annual sales if an unlimited amount is spent on advertising.
a) $600,000 b) $12,000,000 c) $24,000,
d) $400,000 e) $18,000,000 f ) none of the preceding
- A certain product has supply and demand functions given by p = 3.5 q + 20 and p = 650 โ 5.25 q ,
respectively. What price gives the market equilibrium?
a) $72 b) $272 c) $
d) $124 e) $144 f ) none of the preceding
- The Dow Jones index is 12,300 points now. If it could continue to gain 0.1% a day, what would the index be in a year which has 250 trading days?
a) 12,423 b) 15,375 c) 43,
d) 15,791 e) 147,995 f ) none of the preceding
- The profit for a product can be described by the function P ( x ) = 60 x โ 2400 โ 0.05 x^2 dollars, where x is the number of units produced and sold. To maximize profit, how many units must be produced and sold?
a) 600 b) 42 c) 960
d) 15,600 e) 1,158 f ) none of the preceding
- Rewrite 4 ln (2 a ) โ ln b as a single logarithm.
a) (^) โโ โ
b
16 a^4
ln b) ln( 8 a^4 โ b ) c) โโ
b
8 a^4 ln
d) ln( 8 a โ b ) e) โโ
b
2 a^4 ln f ) none of the preceding
- Julian Enterprises has a fleet of 80 vehicles: hybrid passenger cars, vans, and delivery trucks. There are 10 more hybrids than delivery trucks, and four times as many hybrids as vans. How many delivery trucks does Julian Enterprises have?
a) 40 b) 35 c) 30
d) 25 e) 20 f ) none of the preceding
- After McNeill Corp. initiated its fitness program, employee sick days
were recorded for each week following on the table. The Human Resources department thought the decreases might be exponential. Which function best describes the weekly sick days S for each week w after the program started?
a) S ( w ) = 60 ร eโ0.06w^ b) S ( w ) = 60 ร 1.06 โw
c) S ( w ) = 0.06 w^2 โ 2.4 w + 60 d) S ( w ) = 60 ร 0.96 w
e) S ( w ) = 60 โ 1.8 w f ) none of the preceding
Weeks after program
Weekly Sick days 0 60 1 57 2 55 4 51 8 43 12 37 16 31
- The per capita tax burden T (in hundreds of dollars) can be described by T ( t ) = 20.37 + 1.834 t , where
t is the number of years after 1980.
(a) What is the slope of the function?
(b) Interpret the slope as a rate of change.
- A furniture company manufactures antique and baroque chairs which are constructed using wood,
hardware and fabric. The number of units of each material that is required for each product is given in the left table. Because of transportation costs to the companyโs two plants in Pleasantville and Richmond, the unit costs for some of the materials differ. The right table gives the unit costs of the materials at the two plants.
Antique Baroque Wood 2 3 Hardware 3 1 Fabric 8 10
(a) Write the matrix multiplication that shows the cost of manufacturing each type of chair at each plant.
(b) Use part (a) above to find the cost of manufacturing each type of chair at each plant.
- At the end of an advertising campaign, the weekly retail sales of a product declined according to the
equation y = 40,000 (3 โ0.1 x ) dollars, where x is the number of weeks after the campaign ended. Find the weekly sales twelve weeks after the campaign ended.
- A couple has $30,000 for a down payment, and they plan on monthly payments of $2200. If the
interest rate for a 25-year loan is 6% APR, how much can they spend on a house?
Pleasantville Richmond Wood $15 $ Hardware $11 $ Fabric $ 6 $ 7
- Find the inverse of g ( x ) = x^2 โ 3.
- A new dotcom company starts with three owners and five employees, but tells investors that it will
grow rapidly, with the total number of people in the company given by the model
t N = 2000 (. 004 )^0.^5 where t is the number of years from the present. Determine the year in which they predict that the number of employees will be 1000.
* ^ XWXWXWXWXWX*
Formulas:
(1 i ) n 1 S R i
S = Pe r^ t^ 1
kt r S P k
S = P (1 + r ) t^ 1 (1 i ) n A R i
โก โ +^ โ โค
r
a r s
n n (^) โ
(if r โ 1)
n n
n a a s
= an = a 1 + ( n โ 1) d an = a 1 r n โ^^1
